Question

4 The radii of two right circular cylinders are
in the ratio 2:3 and their heights are in the
surface areas and also the ratio of their
ratio 5:4. Calculate the ratio of their curved
volu
volumes
Long hao bogo​

Answer 1

${ \huge{ \bold{\underline{ \underline{ \orange{Correct \: question:-}}}}}}$

The radi of two right circular cylinders are in the ratio 2:3and their heights are in the surface areas and also the ratio 5:4.Calculate the ratio of their curved volumes.

${ \huge{ \bold{\underline{ \underline{ \red{Solution:-}}}}}}$

The ratio of the two right circular cyclinder in the ratio = 2:3.

$\leadsto{\therefore{\tt{\blue{r_1 :r_2 =2:3}}}}$

$\leadsto{\therefore{\tt{\blue{r_1 = 2r}}}}$

$\leadsto{\therefore{\tt{\blue{r_2 = 3r}}}}$

Now,

Let the height be:-

$\leadsto{\therefore{\tt{\purple{h_1 :h_2 =5:4}}}}$

$\leadsto{\therefore{\tt{\purple{h_1 = 5h}}}}$

$\leadsto{\therefore{\purple{\tt{h_2 =4h}}}}$

$\leadsto{\therefore{\tt{\pink{(V_1 ) Volume \: of \: the\: cyclinder = πr^h}}}}$

$\leadsto{\tt{\orange{= π×r^2_1 ×h_1}}}$

$\leadsto{\tt{\orange{= π× 2r × 5h}}}$

$\leadsto{\tt{\orange{= 10π × rh}}}$

$\leadsto{\therefore{\tt{\pink{(V_2 ) Volume \: of \: the\: cyclinder = πr^2h }}}}$

$\leadsto{\tt{\green{= π×r^2_2 ×h_2}}}$

$\leadsto{\tt{\green{= π×3r×4h}}}$

$\leadsto{\tt{\green{= 12π× rh}}}$

A/Q,

$\leadsto{\tt{\blue{\frac{V_1}{V_2} =\cancel\frac{10π× r×h}{12π×r×h}}}}$

$\leadsto{\tt{\blue{\frac{V_1}{V_2} = \frac{5}{6}}}}$

$\leadsto{\therefore{\tt{\blue{V_1 :V_2 = 6:5}}}}$

$\longrightarrow{\tt{\purple{\boxed{V_1:V_2 = 6:5}}}}$